论文信息 - OPTIMALITY CRITERIA FOR MULTIRESPONSE LINEAR MODELS BASED ON PREDICTIVE ELLIPSOIDS

OPTIMALITY CRITERIA FOR MULTIRESPONSE LINEAR MODELS BASED ON PREDICTIVE ELLIPSOIDS

This paper proposes a new class of optimum design criteria for the linear regression model with r responses based on the volume of the predictive ellipsoid. This is referred to as I r L-optimality. The I r L-optimality criterion is invariant with respect to different parameterizations of the model, and reduces to IL-optimality as proposed by Dette and O'Brien (1999) in single response situations. An equivalence theorem for I r L-optimality is provided and used to verify I r L-optimality of designs,

[1] O. Krafft,et al. D-optimal designs for a multivariate regression model , 1992 .

[2] Dennis K. J. Lin,et al. Optimal designs for dual response polynomial regression models , 2001 .

[3] Jürgen Pilz,et al. Bayesian estimation and experimental design in linear regression models , 1992 .

[4] W. Wong,et al. OPTIMAL DESIGNS FOR PARALLEL MODELS WITH CORRELATED RESPONSES , 2006 .

[5] W. J. Studden,et al. Theory Of Optimal Experiments , 1972 .

[6] P. Whittle. Some General Points in the Theory of Optimal Experimental Design , 1973 .

[7] Norbert Gaffke,et al. 30 Approximate designs for polynomial regression: Invariance, admissibility, and optimality , 1996, Design and analysis of experiments.

[8] Huaiqing Wu. Optimal exact designs on a circle or a circular arc , 1997 .

[9] W. G. Hunter,et al. Design of experiments for parameter estimation in multiresponse situations , 1966 .

[10] J. Danskin. The Theory of Max-Min and its Application to Weapons Allocation Problems , 1967 .

[11] M. Berman. Estimating the Parameters of a Circle When Angular Differences are Known , 1983 .

[12] M. Deaton,et al. Response Surfaces: Designs and Analyses , 1989 .

[13] Holger Dette,et al. Optimality criteria for regression models based on predicted variance , 1999 .

[14] F. Pukelsheim. Optimal Design of Experiments , 1993 .

[15] Shing I. Chang. Some Properties of Multiresponse D-Optimal Designs , 1994 .